Question: Ben is 4 times as old as Kevin. Six years ago, Ben was 6 times as old as Kevin. How old is Kevin now?
Solution: We can use the given information to write down two equations that describe the ages of Ben and Kevin. Let Ben's current age be $b$ and Kevin's current age be $k$ The information in the first sentence can be expressed in the following equation: $b = 4k$ Six years ago, Ben was $b - 6$ years old, and Kevin was $k - 6$ years old. The information in the second sentence can be expressed in the following equation: $b - 6 = 6(k - 6)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to use our first equation for $b$ and substitute it into our second equation. Our first equation is: $b = 4k$ . Substituting this into our second equation, we get: $4k$ $-$ $6 = 6(k - 6)$ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $4 k - 6 = 6 k - 36$ Solving for $k$ , we get: $2 k = 30.$ $k = 15$.